Domain and Codomain

A function is an operationthat assigns to each number ina domain, a unique number ina codomain. The function is usually given in the form of an equation,for example, Eachvalue of givesa unique value of -if this were not so, we would not have a function. To sketch afunction we need to find a set of points. This is most easily done bydrawing up a table.


-3

-2

-1

0

1

2

3

9

4

1

0

1

4

9

+1

1

1

1

1

1

1

1

10

5

2

1

2

5

10


If we have a graph of a function and we want to knowthe domain and codomain, then we can find them by looking at theaxes. To find the domain, we look at the x-axis. To find the range orcodomain we look at the-axis. For the function above, the function is restricted tovaluesin the rang [-3,3] so the domain is the interval, [-3,3] and thecodomain or range is the interval [1,10].

The graph below,hasdomain(noticethe vertical dotted line, indicating that atsocannotbe equal to -1) and codomainIfthe graph tends toward anorvaluewithout reaching it, then that value cannot be in the domain orcodomain respectively.

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